1) To make the starter: Mix the starter ingredients in a large bowl. Cover the bowl and let rest at room temperature for 1 hour. The mixture will initially be the consistency of thick pancake batter; after an hour it should be very bubbly, airy, and doubled in size.
2) While the starter rests, ready the dough. Melt the butter over low heat and set it aside to cool. In a small bowl, combine 1 cup of the flour with the sugar, dry milk, salt, and mahlep.
3) Mix 2 of the eggs into the risen starter. Stir in the cooled melted butter.
4) If you're substituting vanilla extract for mahlep, stir it in. Add the flour/sugar mixture and stir until everything is incorporated.
5) Add the remaining 1 1/2 to 2 1/2 cups flour 1 cup at a time, as needed to make dough that's stiff enough to form a ball but is also soft and slightly sticky.
6) Knead the dough — by hand, mixer, or bread machine — until it springs back when pressed gently with a floured finger. If kneading by hand, try to use only the lightest dusting of flour on the counter and on your hands. The more gently you knead, the less sticky the dough will seem. When done, place the dough into a lightly greased bowl, cover with plastic wrap, and refrigerate for 8 to 12 hours, or overnight.
7) The next morning, remove the dough from the fridge and knead it gently a few times, to deflate it.
8) Liberally butter a 9" round cake pan, or line a baking sheet with parchment. Divide the dough into three pieces, and set them aside, covered with lightly greased plastic wrap.
9) If you're using the dyed eggs, rub each one with a paper towel dipped in vegetable oil and set them aside. Press the large piece of dough evenly into the prepared pan.
10) Make three 16" strands with the dough; pinch the ends together at one end. Braid for 4" to 5"; tuck an egg into the braid. Continue to braid, placing another egg into the braid at 2" intervals. You can make a longer, thinner braid with five eggs, the braid formed into a wreath shape and placed in the round pan; or a shorter, straight, thicker braid, using three eggs, as shown above.
11) Cover the pan with lightly greased plastic wrap, and let the loaf rise at room temperature for 2 to 2 1/2 hours; if you're using the round pan, the top of the loaf should be just barely level with the top rim of the pan. During the last 45 minutes of the rise, preheat your oven to 350°F.
12) To bake the bread: Lightly beat the remaining egg. Brush it over the loaf. (Alternatively, omit the egg wash if you'd prefer to brush the loaf with honey when it comes out of the oven.) If you're baking a round loaf, press the last hard-boiled egg firmly into the center of the risen loaf.
13) Bake the bread for 20 minutes. Open the oven door, reach in, and carefully press each egg farther down into the bread.
14) Continue to bake the bread for an additional 40 to 50 minutes, or until the internal temperature reaches 190°F. Tent the bread with aluminum foil for the last 30 minutes, to prevent over-browning.
15) Remove the bread from the oven, and turn it out of the pan onto a rack. If desired, heat 1/4 cup honey with 1 tablespoon water until warm, and brush over the loaf. Let the bread cool completely before serving.
Yield: 1 loaf, 16 slices.